Many real-world problems require reasoning across multiple scales, demanding models which operate not on single data points, but on entire distributions. We introduce generative distribution embeddings (GDE), a framework that lifts autoencoders to the space of distributions. In GDEs, an encoder acts on sets of samples, and the decoder is replaced by a generator which aims to match the input distribution. This framework enables learning representations of distributions by coupling conditional generative models with encoder networks which satisfy a criterion we call distributional invariance. We show that GDEs learn predictive sufficient statistics embedded in the Wasserstein space, such that latent GDE distances approximately recover the $W_2$ distance, and latent interpolation approximately recovers optimal transport trajectories for Gaussian and Gaussian mixture distributions. We systematically benchmark GDEs against existing approaches on synthetic datasets, demonstrating consistently stronger performance. We then apply GDEs to six key problems in computational biology: learning donor-level representations from single-nuclei RNA sequencing data (6M cells), capturing clonal dynamics in lineage-traced RNA sequencing data (150K cells), predicting perturbation effects on transcriptomes (1M cells), predicting perturbation effects on cellular phenotypes (20M single-cell images), designing synthetic yeast promoters (34M sequences), and spatiotemporal modeling of viral protein sequences (1M sequences).

Fairness metrics are a core tool in the fair machine learning literature (FairML),used to determine that ML models are, in some sense, “fair.” Real-world data,however, are typically plagued by various measurement biases and other violatedassumptions, which can render fairness assessments meaningless. We adapt toolsfrom causal sensitivity analysis to the FairML context, providing a general frame-work which (1) accommodates effectively any combination of fairness metric andbias that can be posed in the “oblivious setting”; (2) allows researchers to inves-tigate combinations of biases, resulting in non-linear sensitivity; and (3) enablesflexible encoding of domain-specific constraints and assumptions. Employing thisframework, we analyze the sensitivity of the most common parity metrics under 3varieties of classifier across 14 canonical fairness datasets. Our analysis reveals thestriking fragility of fairness assessments to even minor dataset biases. We show thatcausal sensitivity analysis provides a powerful and necessary toolkit for gaugingthe informativeness of parity metric evaluations. Our repository is \href{https://github.com/Jakefawkes/fragile_fair}{available here}.

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural sciences. While many of these problems stand to benefit from the ability to specify arbitrary, domain-informed constraints, this setting is not covered by the existing (Riemannian) diffusion model methodology. Recent work has attempted to address this issue by constructing novel noising processes based on the reflected Brownian motion and logarithmic barrier methods. However, the associated samplers are either computationally burdensome or only apply to convex subsets of Euclidean space. In this paper, we introduce an alternative, simple noising scheme based on Metropolis sampling that affords substantial gains in computational efficiency and empirical performance compared to the earlier samplers. Of independent interest, we prove that this new process corresponds to a valid discretisation of the reflected Brownian motion. We demonstrate the scalability and flexibility of our approach on a range of problem settings with convex and non-convex constraints, including applications from geospatial modelling, robotics and protein design.